Seiyefa is the erstwhile Director of the Institute of Security Studies (ISS) and the highest ranking director in the Service.
Mr Ibrahim, who belongs to Pro-Saraki group, also protested the invasion of the National Assembly by officers of the Department of State Services and Police Force.
A blockade of Nigeria's parliament on Tuesday by security forces that prevented lawmakers from entering for up to an hour was done without the presidency's knowledge, said the acting president, who sacked the head of the security agency.
Before his new appointment, he was Daura's deputy, being the most senior director in the DSS.
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Atiku, who is a PDP presidential hopeful, urged Buhari to call the police and DSS to order "and abandon this madness".
After meeting with Osinbajo, he left the villa without speaking with reporters.
A statement by the NBA President, Abubakar Balarabe Mahmoud (SAN) said, "The Nigerian Bar Association condemns this brazen and blatant act of the security personnel and demands the immediate withdrawal of this personnel".
The Federal Government has named the most senior director in the Department of State Service (DSS), Matthew Seiyefa, as the acting Director-General of the service. "Seiyefa is also a member of the National Institute". Parliament went on recess last week until September 25 but meetings were to be held on Tuesday.
The Acting President, Professor Yemi Osinbajo, has condemned what he described as an unauthorized takeover of the national assembly complex by security operatives on Tuesday.